{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YMMYCQGSDZMDV2JAGOFI7SECLE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a29d8c5550fde2677a89e60e2dda6bde1e5378b053f9b1806ec72df9de4f6c25","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-09-14T00:37:59Z","title_canon_sha256":"7d293343dc536bedb76dd380b0b5dbd72652ee6bc530d4b5026789e1aa8403b0"},"schema_version":"1.0","source":{"id":"0909.2442","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2442","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2442v2","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2442","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"YMMYCQGSDZMD","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YMMYCQGSDZMDV2JA","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YMMYCQGS","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:27ca92132f2bd68ae171530e4454a0c5e513a82d22d6c3b4ea9a700b6876a9fe","target":"graph","created_at":"2026-05-18T04:30:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We provide the unique affine crystal structure for type E_6^{(1)} Kirillov-Reshetikhin crystals corresponding to the multiples of fundamental weights s Lambda_1, s Lambda_2, and s Lambda_6 for all s \\geq 1 (in Bourbaki's labeling of the Dynkin nodes, where 2 is the adjoint node). Our methods introduce a generalized tableaux model for classical highest weight crystals of type E and use the order three automorphism of the affine E_6^{(1)} Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type E_7^{(1)} Kirillov-Reshetikhin crystals corresponding to the adjo","authors_text":"Anne Schilling, Brant Jones","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-09-14T00:37:59Z","title":"Affine structures and a tableau model for E_6 crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2442","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:07955a093d97c757432d3105701cedf0eb8d32923d4acef650ca195f9ca97e75","target":"record","created_at":"2026-05-18T04:30:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a29d8c5550fde2677a89e60e2dda6bde1e5378b053f9b1806ec72df9de4f6c25","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-09-14T00:37:59Z","title_canon_sha256":"7d293343dc536bedb76dd380b0b5dbd72652ee6bc530d4b5026789e1aa8403b0"},"schema_version":"1.0","source":{"id":"0909.2442","kind":"arxiv","version":2}},"canonical_sha256":"c3198140d21e583ae920338a8fc8825932b6d44f3bd2dd402f706ccf5212d378","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3198140d21e583ae920338a8fc8825932b6d44f3bd2dd402f706ccf5212d378","first_computed_at":"2026-05-18T04:30:03.873928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:03.873928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LK76RujCG0Y/YThlTiTw4dD8T7DzV8U9vlPXM3f8VE5pQl1hOPVwYcEUEoVYVpcb+OZf4ZdOgSRIiQaVUWjnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:03.874304Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2442","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07955a093d97c757432d3105701cedf0eb8d32923d4acef650ca195f9ca97e75","sha256:27ca92132f2bd68ae171530e4454a0c5e513a82d22d6c3b4ea9a700b6876a9fe"],"state_sha256":"f57f5c1fc9723e5fe286f033a85ef93185966b714b8ac883ce2cba0ee9103163"}